Conformal Mapping of Nonsmooth Domains via the Kerzman]Stein Integral Equation

The connection between the Riemann map and the Szeg˝o kernel is classical. But the fact that there is an efficient numerical procedure, based on the Kerzman]Stein integral equation, for computing the Szeg˝o kernel of a smoothly bounded domain in the plane is more recent. In this paper it is shown how to extend the results of Kerzman and Stein to certain nonsmooth domains. This provides a new method for numerically computing the Szeg˝o kernel, and hence the Riemann map, of these domains